Approximation in Lp(Rd) from spaces spanned by the perturbed integer translates of a radial function

[摘要] The problem of approximating smooth L-p-functions from spaces spanned by the integer translates of a radially symmetric function phi is very well understood. In case the points of translation, Xi, are scattered throughout R-d, the approximation problem is only well understood in the stationary setting. In this work, we provide lower bounds on the obtainable approximation orders in the non-stationary setting under the assumption that Xi is a small perturbation of Z(d). The functions which we can approximate belong to certain Besov spaces. Our results, which are similar in many aspects to the known results for the case Xi = Z(d), apply specifically to the examples of the Gauss kernel and the generalized multiquadric. (C) 2000 Academic Press.

[发布日期] 2000-12-01